# An angle measures 160° more than the measure of a supplementary angle. What is the measure of each angle?

May 17, 2018

The two supplementary angles are $10$ and $170$ degrees.

#### Explanation:

Two angles are supplementary when that add up to $180$ degrees. In this case, we are given that one of the two angles is $160$ degrees more than the other. We can construct the following equation.

$x + \left(x + 160\right) = 180$

$x$ represents the degree measure of the smaller angle. Now, all we need to do is solve the equation for $x$.

$2 x + 160 = 180$

$2 x = 20$

$x = 10$

Now that we have the value of the smaller angle, we can easily solve for the larger angle. We are told that it is $160$ degrees larger than the other one.

$10 + 160 = 170$

Therefore, the two supplementary angles are $10$ and $170$ degrees.